An apparatus for image coding includes a processor to: execute a determining process that includes, when a specific entry included in a first palette for use in coding a first block in a coding-target image is not an entry candidate for a second palette for use in coding a second block to be coded after the first block, determining an entry to be included in the second palette based on a first index indicating a code amount to be generated when the specific entry is to be included in the second palette and a second index indicating a code amount to be generated when the specific entry is not to be included in the second palette; execute a generating process that includes generating the second palette including the entry determined in the determining process; and execute a palette coding process that includes coding the second block by the second palette.